Astrophysical observations provide strong evidence for the existence of black holes. However, it remains an open question whether some exotic compact objects, capable of mimicking black holes observationally, might be responsible for the observed phenomena. In this talk, I will discuss possible methods to distinguish black holes from other compact objects using gravitational wave signals from compact binary mergers. I will focus on one such test, which leverages the fact that black holes absorb energy and angular momentum from binary orbits due to the presence of their horizons. I will outline the implications of this effect for current and future ground-based gravitational wave detectors and emphasize the importance of incorporating it into gravitational waveform modeling.